Luke Gallows did an interview with NOLA.com recently and when asked about the name of his crew, The Club, he had this to say about knowing they had to drop the “Bullet" part of it:
"Yeah, we kind of knew that. We were being edgy in Japan (with The Bullet Club), and there's a bit of a language barrier. The WWE is all about family friendly entertainment. My son and I watch the WWE Network at home all the time. Going with The Club was the way we needed to go to come here and be in this environment, where your kids are watching."
Obviously, WWE was never going to use “Bullet Club” because they don’t have the rights to it but even if they did it seems unlikely the company would promote a faction with that name. Sometimes the simplest solution is best.
Even if it's not all that creative.